Optimizing Rice Cookers Using Fuzzy Logic: An Application Approach

Optimizing Rice Cookers Using Fuzzy Logic: An Application Approach

Adrian Dwi Nurcahyo Nugroho

Mathematics Department, Faculty of Mathematics and Natural Sciences, Yogyakarta State University Universitas Negeri Yogyakarta

E-mail : adriandwi.2020@student.uny.ac.id

Abstract. Fuzzy logic is related to the formal principles of approximate reasoning, where it does not deal with exact values. Variables in fuzzy logic have truth values between 0 and 1. The reasoning in fuzzy logic is similar to human reasoning, such as when operating household appliances. This can be utilized by implementing fuzzy logic in household appliances to make them more efficient and effective.

INTRODUCTION

Fuzzy logic is a logic system used in technology that has found widespread application in everyday life. Many household appliances utilize fuzzy logic in their chips to enhance their effectiveness. One such appliance is the vacuum cleaner, which has been sold with the incorporation of fuzzy logic. Fuzzy logic in vacuum cleaners is used to regulate the suction power for dust cleaning. The use of fuzzy logic in vacuum cleaners can help save energy consumption. In addition to vacuum cleaners, there are many other household appliances that can benefit from the addition of fuzzy logic. Examples include washing machines, televisions, air conditioners, ovens, and many more.

By implementing fuzzy logic, these appliances can become more efficient and effective in their operations.Rice cookers, or rice steamers, are also important household appliances in daily life. The most significant benefit of a rice cooker is time efficiency.

In cooking rice, there are five stages involved:

absorbing water, heating, boiling, stewing, and holding.

Fig 1. Stage In Cooking Rice In general, the process of cooking rice in a rice cooker involves two functions: cooking and heating. During the cooking or heating process, electric current flows to their respective heating elements. The cooking time for rice can vary; some may take a long time, while others may be faster. One important aspect we can learn from a rice cooker is the time required to cook rice. The cooking time of a rice cooker depends on two factors: the amount of water and rice used. This paper will discuss the utilization of fuzzy logic in rice cookers, a household appliance.

RESEARCH METHOD

This study is centered around the duration of rice cooking using a rice cooker. The required cooking time is contingent upon the quantities of rice and water utilized. The research procedure is outlined as follows:

a. Determine the input and output of the system, as well as the universe of discourse for each variable.

In this instance, two input variables are employed, namely the water quantity and rice quantity, while the output variable is the duration of rice cooking. The universal sets for the water quantity and rice

quantity variables are [0,10] and [0,100] respectively, while the universal set for the cooking time variable is [0,80].

b. Establish the number of fuzzy sets for each input and output, along with the membership functions.

Each input variable will be defined with three fuzzy sets, whereas the output variable will consist of five fuzzy sets utilizing trapezoidal and triangular membership functions.

c. Define the fuzzy rules and determine the rule composition of the system (inference system). The inference system employed is Max Min.

d. Execute the defuzzification process using the centroid method.

By following these steps, the objective of this research is to enhance the efficiency of rice cooking time in a rice cooker through the application of fuzzy logic.

Hasil dan Pembahasan

A fuzzy control scheme for rice cooking time can be depicted as follows:

This paper will utilize two inputs, namely the amount of water and the amount of rice used. The characteristics of the amount of water can be divided into three categories: low, medium, and high. Similarly, the amount of rice used also has three characteristics: low, medium, and high. The output result of the cooking time by the rice cooker will have five variables, which are as follows:

 Very short cooking time

 Short cooking time

 Moderate cooking time

 Long cooking time

 Very long cooking time

Let's denote the amount of water used as 'a' within the interval [0,10]. The amount of water used can be represented in a triangular membership function. The numbers in Figure 2 below represent the amount of water used in linguistic variables, with the linguistic variable base denoted as 'a'. Let's denote the linguistic variable as 'A' with its membership functions.

S

_a

(x )= { ^{3− 3 0, x another , 0 ≤ x ≤3 , M}

^a

^{( x )=} { ^{8− x−2 3 3 0, x another , , 2 5 ≤ x ≤ ≤ x ≤ 5 8 , B}

^a

^{( x )= { x −7 3 0, another , 7 ≤ x ≤ 10}

FUZZY

CONTROLLER

l

TIMER R COOKE RICE

a r

Fig 2. Timeline Cooking Rice Fuzzy Control Scheme

Fig 3. Input Variable “Banyak Air”

The linguistic variable A represents the three choices for the level of water quantity: low ( S_a ), medium (

M

_a ), and high (

B

_a ). These three options are part of the linguistic variable A, which represents the amount of water used.

Assuming the amount of rice used is denoted as 'r' within the interval [0,100]. The amount of rice used can be categorized into three units: low ( S_r ), medium ( M_r ), and high ( B_r ). These three linguistic units are represented in a trapezoidal graph, as shown in Figure 3 below. The numbers on the graph indicate the amount of rice used in linguistic variables, with the linguistic variable base denoted as 'r'. Let's denote the linguistic variable as 'R' with its membership functions.

S

_r

( x )= { ^{40− 20 1,0 0,another x , ≤ x ≤ 20 ≤ x ≤ 20 40 M}

^r

^{( x)=} { ^{80− x−20 20 20 1, 40 0, x another ,20 , ≤ x ≤ 60≤ x ≤ ≤ x ≤ 60 40 80}

B

_r

( x )= { ^{x−60 20 1, 80 0, another ,60 ≤ x ≤100 ≤ x ≤ 80}

Fig 4. Input Variabel amount of rice

Fuzzy numbers represent three options for saturation time: low ( S_r ), medium ( M_r ), and high ( B_r ).

These three choices are part of the linguistic variable R representing the required cooking time (denoted as t) and T as the linguistic variable. It is assumed that t∈[0,80], and the machine's control system is designed to

differentiate the required time into five categories: very short (

VS

_t ), short (

S

_t ), medium (

M

_t ), long ( L_t ), and very long ( V L_t ). These linguistic statements are defined in Figure 4 with their membership functions:

VS

_t

( x)= { ^{20− 20 0, x another ,0 ≤ x ≤ 20 S}

^t

^{( x )=} { ^{40− 20 20 x 0,another x ,0 ,20 ≤ x ≤ ≤ x ≤ 20 40}

M

_t

(x )= { ^{60− x−20 20 20 0, x another , , 20 40 ≤ x ≤ ≤ x ≤ 40 60}

L

_t

( x )= { ^{x− 80− 20 20 40 0, x another , ,60 40 ≤ x ≤ ≤ x ≤ 60 80}

VL

_t

( x)= { ^{x−60 20 0, another , 60≤ x ≤ 80}

Fig 5. Output Variabel Cooking time

From Figure 4, the fuzzy numbers represent the five choices for the required cooking time by the rice cooker: very

short

VS (¿¿ t )

¿

,, short

(S

_t

)

,, medium ( M_t ), long ( L_t¿ ,, and very long ( VL_t ). These five choices are part of the linguistic variable

T

The decisions provided by the fuzzy controller are derived from the rules in the knowledge base. There are 9 rules that will generate the output, as follows:

1) IF Amount of water is Low AND Amount of rice is Small THEN Cooking time is Short 2) IF Amount of water is Medium AND Amount of rice is Small THEN Cooking time is Medium 3) IF Amount of water is High AND Amount of rice is Small THEN Cooking time is Long 4) IF Amount of water is Low AND Amount of rice is Medium THEN Cooking time is Medium 5) IF Amount of water is Medium AND Amount of rice is Medium THEN Cooking time is Medium 6) IF Amount of water is High AND Amount of rice is Medium THEN Cooking time is Long

7) IF Amount of water is Low AND Amount of rice is Large THEN Cooking time is Medium 8) IF Amount of water is Medium AND Amount of rice is Large THEN Cooking time is Long 9) IF Amount of water is High AND Amount of rice is Large THEN Cooking time is Long

Table 1, which contains the set of rules, provides the output of the cooking time in the rice cooker machine.

Rice Amount

t ^{Small Medium Large}

Banyaknya Air Low Very Short Short Medium

Medium Short Medium Long

High Medium Long Very

Long Table 1.Rule

Manual Calculation

Manual calculation method to determine the output value of t can be done in four steps. For each value of the variables d and s, the controller determines the appropriate value for the variable t by following these operational steps :

1. Let's consider the following values: â = 5, defined in A = S_a, M_a, B_a, with membership degrees μ(S_a) = 0, μ(M_a) = 1, and μ(B_a) = 0. Similarly, r̂ = 50 is defined in R = S_r, M_r, B_r, with membership degrees μ(S_r)

= 0, μ(M_r) = 0.6, and μ(B_r) = 0. This means that only the variables M_a and M_r are used because only rules with non-zero values can be processed in determining the control variable. Hence, the rules used are indicated in red in Table 1.

Fig 6. The membership degrees for the given values are a=5^ ^and r=50^ 2. Inferensi made based from rule, In this example function will be

∫

20 60

C

_{^a ,b^}

(t )dx = ∫

20

32

( ^{t −20} 20 ) ^{dt + ∫}

₃₂⁴⁸

^{( 0.6) dt + ∫}

₄₈⁶⁰

( ^60−t 20 ) ^{dt = 84} 5

Fig 7. Inferensi rule for value a=5^ and r=50^

3. In general, the fuzzy set C(â, r̂) with its membership function defined for each t ∈ [0,80] applies,

C

_{^a ,r^}

(t )=max { ^{min [ M}

^a

^{( ^ a ) , M}

^r

^{( ^ r ) , M}

^t

^{(t ) ]} }

Fig 8. The fuzzy set representing the general conclusion based on the input data â

= 5 and r̂ = 50, as well as the output data t̂, can be defined.

4. Defuzzification

t = The value of theintegral of the product between t∧each individual function isC

_{a ,^ ^r}

(t ) The area underthe graph representstheintegral value. C

_{^a ,r^}

(t )

t=

∫

20 60

t C_{a ,^ ^r}

(

t

)

dt

∫

20 60

C_{^a ,r^}

(

t

)

dt

The numerator value in the above calculation is

∫

20 60

tC

_{a ,^ ^r}

( t) dx= ∫

20 32

t ( ^{t −20} 20 ) ^{dt + ∫}

₃₂⁴⁸

^{t ( 0.6 )dt + ∫}

⁶⁰₄₈

( ^60−t 20 ) ^{dt = 3252} 5

The denominator value in the above calculation is

∫

20 60

C

_{^a ,r^}

( t ) dx= ∫

20

32

( ^t−20 20 ) ^{dt + ∫}

₃₂⁴⁸

^{( 0.6) dt + ∫}

₄₈⁶⁰

( ^60−t 20 ) ^{dt = 84} 5

Therefore, the obtained value is

t ^ = 3252

5 84

5

= 271 7 =38,7

Computational Calculation

Since two inputs are being used here, namely the amount of water and the amount of rice, it requires two input menus and one output menu.

Fig 9. Menu view of input dan output

Based on the given inputs of the amount of water and the amount of rice, and the desired output of the cooking time of rice, you can create rules that capture the relationships between these variables.

a. Water amount

Fig 10. Input view of water amount b. Rice amount

Fig 11. input view rice amount c. Cooking Time

Fig 12. Output view Cooking Time

Once the input and output variables have been defined, the next step is to establish the rules.

Fig 13. Rule Editor and Rule Viewer

It can be observed that with the input values â = 5 and r̂ = 50, the output value t̂ is 40. Figure 14 displays the results on a 3D graph generated using Matlab. The results demonstrate that the machine responds differently to various conditions..

Gambar 14. View of Surface Viewer

Conclusion

Fuzzy logic has been applied in a simulation of a rice cooker. By using different amounts of water and rice, the cooking time can be adjusted accordingly. In the simulation, when 5% water and 50% rice were used, the cooking time was around 40%. This means that it took 40% of the total cooking time to effectively cook rice with those specific quantities. This demonstrates that fuzzy logic in a rice cooker can make the cooking process more efficient. Although

this study focused on two input variables, water and rice quantities, it provides a good representation of the potential benefits of using fuzzy logic in rice cookers.

REFERENCE

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